Statprob

Statistical Experiment

Statistical Experiment

process that generates outcomes or observations, typically with uncertainty involved

Random Experiment

an experiment whose outcome cannot be predicted

Sample space

set of all possible outcomes

Sample point

an element of sample space

Random

unpredictable or unidentified

Variable

symbol, can take on any of a specified set of values

Random variable

• Stochastic variable

• rule that assigns a numerical value or characteristic

Two types of random variable

• Discrete

• Continuous

Discrete random variable

countable, finite can be obtained by counting

Continuous random variable

measurement, infinite, interval

Range space

set of all possible values in a random variable

Discrete Probability Distribution

• also known as Probability Mass Function

• a table that gives a list of probability values along with their associated value in the range of a discrete random variable

• sum of all probability values always equal to 1

Probability Histogram

figure or diagram that contains rectangles centered at each mass point

Expected values

also known as “expectation or payoff value”

is the mean of the probability distribution of the given random variable

Variance

measures the degree of spread of the different values of the random variable about its expected value or mean

tree diagram

a visual tool that makes use of branching connecting lines to represent a certain relationship between the events

horizontal axis

represents the values of the random variable X

vertical axis

gives the corresponding probabilities, P(X)

Mean of a Discrete Random Variable

It is the central value or average of its corresponding probability mass function.

Variance and Standard Deviation of a Discrete Random Variable

describe how scattered or spread out the scores are from the mean value of the random variable.

higher chance of losing

A value of negative indicates that there is a _____

gain

A positive value of indicates a ____ from the deal

normal distribution

• is a probability density function for a continuous random variable.

• It is also known as the Gaussian distribution in honor of the German Mathematician who derived its equation

Johann Carl Friedrich Gauss

German Mathematician who derived Gaussian distribution

Three Types of Kurtosis

• Leptokurtic

• Mesokurtic

• Platykurtic

Leptokurtic

is a distribution where values are clustered heavily or pile up in the center.

Mesokurtic

is an intermediate distribution which are neither too peaked nor too flat.

Platykurtic

is a flat distribution with values more evenly distributed about the center with broad humps and shot tails.

Inflection points

are the points that mark the change in the curve’s concavity.

Standard Normal Distribution

Is a special normal distribution whose mean is equal to 0 and the standard deviation is 1

z-table

• The table used to summarize the approximate areas under the standard normal curve, given in four decimal places.

• The values given in the table represents the area under the standard normal curve from 0 (the mean).

Population

• refers to the entire group of individuals or objects known to have similar characteristics.

• the totality of observations or elements from a set of data.

Sample

• a subset of the entire population

• refers to one or more elements taken from the population for a specific purpose.

Statistic

a numerical measure or value that describes a sample

Parameter

a numerical measure that describes a characteristic of an entire population.

Probability Sampling

• Simple random

• Systematic

• Stratified

• Cluster

Nonprobability Sampling

• Convenience

• Purposive

• Snowball

• Quota

Simple Random Sampling

• use a sampling frame, a list of individuals in the population

• also know as “lottery method”, the most commonly used sampling technique

• every element of the population has the same probability of being selected for the inclusion in the sample

Systematic Sampling

• adopts a skipping pattern in the selection of sample units

• every kth member of the population is selected until the desired number of elements in the sample is obtained

Stratified Sampling

• the population is partitioned into subgroups called strata, based on some characteristics like year, religion, gender, age, ethnicity, etc.

• samples are then randomly selected separately in each stratum

Cluster Sampling

• the total population is divided into clusters that can be pre-existing designation as to cities, towns or provinces.

• used when "natural" but relatively heterogeneous groupings are evident in a statistical population.

• A random sample of clusters will be taken and all individuals in the selected cluster will be part of the sample

Convenience Sampling

• known as grab or opportunity sampling or accidental or haphazard sampling

• involves the sample being drawn from that part of the population which is close to hand. That is, readily available and convenient.

Purposive Sampling

• done with a purpose in mind

• also called judgmental or selective sampling, focuses on samples which are taken based on the judgment of the researcher

Snowball Sampling

• sometimes called chain-referral sampling.

• the researcher chooses a possible respondent for the study at hand. Then each respondent is asked to give recommendations or referrals to other possible respondents.

• used when the research is focused on participants with very specific characteristics such as being members of a gang, victims of domestic violence, etc.

Quota Sampling

• equivalent of stratified random sampling in terms of nonprobability sampling.

• the researcher starts by identifying quotas, which are predefined control categories such as age, gender, education, or religion.

Sampling Distribution

refers to the probability distributions of statistics, considering that the sample mean may vary from sample to sample

Central Limit Theorem

States that as the sample size n increases, the distribution of the sample means taken with replacement from a population approaches a normal distribution